Per BBC Sport, the Gunners inquired about the 29-year-old on Monday, but were rebuffed.
Reports of a £60 million offer emerged just hours before Villa's Champions League victory over Celtic, where Watkins scored but missed a penalty.
On Watkins, manager Unai Emery stated: "I don't want. Every player can be in the market in case it's good for the player, the club and the team. But to get this deal we are going to be very demanding as well and Watkins is our striker."
Asked about the timing of Arsenal's approach, Emery added: "For me it doesn't matter... it's most important how the players respond.
“We have a lot of speculation around the players in the squad but they're showing us they are mature and responsible."
On striker Jhon Duran possibly leaving for Al Nassr, he added: "If he's leaving it's good news for us because they're paying good money and we developed him in two years".